Re-Entry Question

[nafxos]

I was the BU for a JV game last Friday and the following re-entry question arose. Bottom of the 4th, home team sends up a pinchhitter (we'll call him "Adams") to bat for F3 (we'll call him "Brown") in the leadoff spot in the batting order. In the top of the 5th, Brown remains in the field to play first base. Adams goes back to the bench, never playing in the field. In the bottom of the 5th, the home team sends Adams up to pinch hit again in the 5th spot in the lineup. Visiting HC freaks out, saying he can't bat twice in the same turn through the lineup. We confer for a few minutes and the PU decides to let Adams bat. (He struck out on 4 pitches, but that's beside the point.)

Adams was batting the second time because a player became unavailable (he had actually left the field for personal reasons, but it could have just as easily been an injury situation) and they had nobody else on the bench.

So, the question is: can Adams bat twice in the same turn through the lineup? If not, what happens in the #5 spot when that hitter is unable to bat and Adams is the only available pinchhitter?

We play under modified OBR rules with re-entry allowed, but I've never actually seen the re-entry rule written down anywhere.